SEQUENCES AND SERIES: arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series; sigma notation
COMBINATORICS: counting principles, including permutations and combinations; binomial theorem: expansion of (a + b)n
FUNCTIONS: Concept of function f(x) : domain, range; image (value); composite functions f o g ; identity function; inverse function f−1; the graph of a function; its equation y = f(x); function graphing skills: use of a GDC to graph a variety of functions; investigation of key features of graphs; solutions of equations graphically; transformations of graphs: translations; stretches; reflections in the axes; the graph of y = f−1(x) as the reflection in the line y = x of the graph of y = f(x); the graph of 1 / f(x) from y = f(x); the graphs of the absolute value functions, y =| f(x) | and y = f( |x| ); the reciprocal function f(x) = 1 / x, x≠ 0: its graph; its self-inverse nature; inequalities in one variable, using their graphical representation; the factor and remainder theorems, with application to the solution of polynomial equations and inequalities.
QUADRATICS: the quadratic function f(x) = ax2 + bx + c : its graph; axis of symmetry x = –b / 2a ; the form a(x – h)2 + k; the form a(x – p)(x – q); the solution of ax2 + bx + c = 0, a ≠ 0; the quadratic formula; use of the discriminant ∆ = b2 – 4ac
CIRCLES AND TRIGONOMETRY: the circle: radian measure of angles; length of an arc; area of a sector; Solution of triangles: cosine rule, sine rule, area of triangle as 1/2 ab sin C
CALCULUS: informal ideas of limit and convergence; differentiation by first principles, derivative of xn, derivative interpreted as a gradient function and as a rate of change; differentiation of a sum and a real multiple of functions; the second and higher derivatives; local maximum and minimum points; use of the first and second derivatives in optimization (max/min) problems; indefinite integration as anti-differentiation; indefinite integral of xn; anti-differentiation with a boundary condition to determine the constant term; definite intergrals; area between a curve and the x-axis and y-axis in a given interval; areas between curves; kinematic problems involving displacement, velocity and acceleration; the significance of the second derivative; distinction between maximum and minimum points; points of inflexion with zero and non-zero gradients
SEQUENCES AND SERIES: arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series; sigma notation
COMBINATORICS: counting principles, including permutations and combinations; binomial theorem: expansion of (a + b)n
FUNCTIONS: Concept of function f(x) : domain, range; image (value); composite functions f o g ; identity function; inverse function f −1; the graph of a function; its equation y = f(x); function graphing skills: use of a GDC to graph a variety of functions; investigation of key features of graphs; solutions of equations graphically; transformations of graphs: translations; stretches; reflections in the axes; the graph of y = f −1(x) as the reflection in the line y = x of the graph of y = f(x); the graph of 1 / f(x) from y = f(x); the graphs of the absolute value functions, y =| f(x) | and y = f( |x| ); the reciprocal function f(x) = 1 / x, x≠ 0: its graph; its self-inverse nature; inequalities in one variable, using their graphical representation; the factor and remainder theorems, with application to the solution of polynomial equations and inequalities.
QUADRATICS: the quadratic function f(x) = ax2 + bx + c : its graph; axis of symmetry x = –b / 2a ; the form a(x – h)2 + k; the form a(x – p)(x – q); the solution of ax2 + bx + c = 0, a ≠ 0; the quadratic formula; use of the discriminant ∆ = b2 – 4ac
CIRCLES AND TRIGONOMETRY: the circle: radian measure of angles; length of an arc; area of a sector; Solution of triangles: cosine rule, sine rule, area of triangle as 1/2 ab sin C
CALCULUS: informal ideas of limit and convergence; differentiation by first principles, derivative of xn, derivative interpreted as a gradient function and as a rate of change; differentiation of a sum and a real multiple of functions; the second and higher derivatives; local maximum and minimum points; use of the first and second derivatives in optimization (max/min) problems; indefinite integration as anti-differentiation; indefinite integral of xn; anti-differentiation with a boundary condition to determine the constant term; definite intergrals; area between a curve and the x-axis and y-axis in a given interval; areas between curves; kinematic problems involving displacement, velocity and acceleration; the significance of the second derivative; distinction between maximum and minimum points; points of inflexion with zero and non-zero gradients